Extreme ultraviolet (EUV) lithography is a leading candidate for the next-generation lithographic solution. The current optical irradiation wavelength for EUV lithography is 13.5 nm. The prototypes operational in the field have demonstrated the feasibility of fabricating 32- and 22-nm node devices. Unlike deep ultraviolet (DUV) lithography systems such as the 193 nm system, EUV lithography systems cannot use refractive optical elements because of strong material absorption at the EUV wavelength. Instead, reflective optical elements such as mirrors are needed. EUV masks also need to work in a reflective mode.
A typical EUV projection printing system includes multiple mirrors. At the mask plane, the chief ray is off-axis by roughly 6 degrees but is perpendicular to the image plane (wafer plane). Thus, the system is telecentric at the wafer plane, but non-telecentric at the mask plane. The illuminated field on the mask plane is arc-shaped spanning about ±22 degrees from the plane of incidence, as illustrated in FIG. 3a. The plane of incidence is defined by the surface normal of the mask plane and the illumination light ray. The size of the illuminated field is about 1×22 mm2. The combination of non-telecentricity at the mask plane and mask topography cause a unique problem for the EUV lithography—the mask shadowing effect. The mask shadowing effect is schematically shown in FIG. 3b. Shadows are formed around patterns represented by the absorber shapes and make them wider in the near field image of the mask. This mask pattern widening is passed on to the wafer image through the imaging optics. The mask shadowing effect is asymmetric with respect to horizontal and vertical features. As a result, critical area (CD) bias and position shift will occur if not corrected.
As with other systematic patterning errors, the shadowing effect should be compensated for in the EUV lithographic process. Conventional compensation methods may be rule based or model based. In a simple rule-based method, for example, a single bias correction to all features is applied. This method does not take account of variations of the shadowing effect across the illuminated field, i.e., the azimuthal angle dependence of the shadowing effect. Moreover, most rule-based compensation methods are empirically developed with simple Manhattan patterns and thus do not work well with complicated geometric patterns. Rigorous modeling of the mask shadowing effect can provide better correction results. They are, however, computationally expensive and thus impractical in many applications. Therefore, it is desirable to develop an efficient method for modeling and correcting the mask shadowing effect.